Quantum Physics

Title:
Quantum trade-off coding for bosonic communication

Abstract: The trade-off capacity region of a quantum channel characterizes the optimal
net rates at which a sender can communicate classical, quantum, and entangled
bits to a receiver by exploiting many independent uses of the channel, along
with the help of the same resources. Similarly, one can consider a trade-off
capacity region when the noiseless resources are public, private, and secret
key bits. In [Phys. Rev. Lett. 108, 140501 (2012)], we identified these
trade-off rate regions for the pure-loss bosonic channel and proved that they
are optimal provided that a longstanding minimum output entropy conjecture is
true. Additionally, we showed that the performance gains of a trade-off coding
strategy when compared to a time-sharing strategy can be quite significant. In
the present paper, we provide detailed derivations of the results announced
there, and we extend the application of these ideas to thermalizing and
amplifying bosonic channels. We also derive a "rule of thumb" for trade-off
coding, which determines how to allocate photons in a coding strategy if a
large mean photon number is available at the channel input. Our results on the
amplifying bosonic channel also apply to the "Unruh channel" considered in the
context of relativistic quantum information theory.

Comments:

20 pages, 7 figures, v2 has a new figure and a proof that the regions are optimal for the lossy bosonic channel if the entropy photon-number inequality is true; v3, submission to Physical Review A (see related work at this http URL); v4, final version accepted into Physical Review A